A Uniqueness Theorem for a Delay-Differential System

SIAM Review ◽  
1967 ◽  
Vol 9 (4) ◽  
pp. 737-740 ◽  
Author(s):  
Robert M. Bullock
Keyword(s):  
Uniqueness Theorem ◽  
Differential System ◽  
Delay Differential System ◽  
Delay Differential

scholarly journals Applications of Legendre spectral collocation method for solving system of time delay differential equations

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402092211
Author(s):  
Sami Ullah Khan ◽  
Ishtiaq Ali
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Collocation Method ◽  
Differential System ◽  
Numerical Test ◽  
Spectral Collocation Method ◽  
Numerical Techniques ◽  
Spectral Collocation ◽  
Delay Differential System ◽  
Delay Differential

The numerical techniques are regarded as the backbone of modern research. In literature, the exact solution of time delay differential models are hardly achievable or impossible. Therefore, numerical techniques are the only way to find their solution. In this article, a novel numerical technique known as Legendre spectral collocation method is used for the approximate solution of time delay differential system. Legendre spectral collocation method and their properties are applied to determined the general procedure for solving time delay differential system with detail error and convergence analysis. The method first convert the proposed system to a system of ordinary differential equations and then apply the Legendre polynomials to solve the resultant system efficiently. Finally, some numerical test problems are given to confirm the efficiency of the method and were compared with other available numerical schemes in the literature.

scholarly journals Generic oscillations of delay differential system with impulses

2003 ◽  
Vol 45 (4-5) ◽  
pp. 615-622 ◽  
Author(s):  
Yongrui Duan ◽  
Peng Tian ◽  
Weiping Zhang ◽  
Wei Feng
Keyword(s):  
Differential System ◽  
Delay Differential System ◽  
Delay Differential

Positive Solutions for the nth-Order Delay Differential System with Multi-Parameter

2011 ◽  
Vol 50-51 ◽  
pp. 185-189
Author(s):  
Qiu Ying Lu ◽  
Wei Peng Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Differential System ◽  
Point Theorem ◽  
Nonlinear Eigenvalue Problem ◽  
Existence Of Positive Solutions ◽  
Delay Differential System ◽  
Delay Differential ◽  
Nonlinear Eigenvalue

In this paper, we are concerned with the existence of positive solutions for the nonlinear eigenvalue problem of the nth-order delay di erential system. The main results in this paper generalize some of the existing results in the literature. Our proofs are based on the well-known Guo-Krasnoselskii xed-point theorem. Three main results are given out, the rst two of which refer to the existence while the last one not only guarantees to its existence but also is pertinent to its multiplicity.

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